Question 461045
Denote the square root by sqrt(x), "check" is too ambiguous.


To simplify square roots, you have to factor perfect squares out. To factor


*[tex \LARGE -\sqrt{20} + 2\sqrt{18}],


we see that the largest perfect square divisor of 20 is 4, and for 18, it is 9. So,


*[tex \LARGE -\sqrt{20} + 2\sqrt{18} = -\sqrt{4*5} + 2\sqrt{9*2}]


Now we split the 4 and the 5, as well as the 9 and the 2.


*[tex \LARGE = -2\sqrt{5} + 2(3 \sqrt{2})]


*[tex \LARGE = -2\sqrt{5} + 6\sqrt{2}]